Name Chemistry / / Gas Laws Dalton, Boyle, Charles, Gay-Lussac & Avogadro gas laws

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1 Name Chemistry / / Gas Laws Dalton, Boyle, Charles, Gay-Lussac & Avogadro Today we will begin our investigation into the wonderful world of gas laws. Basically we will be looking at the different ways a gas reacts when temperature, pressure and volume are changed. The first thing you need to be aware of is that when solving gas law problems temperature must always be in Kelvin (K). To convert Celsius to Kelvin add 273 (K = C + 273). Standard temperature is 0 ºC or 273 K. Volume should be in liters(l), cubic decimeters (dm 3 ), milliliters(ml) or cubic centimeters(cm 3 ), whichever is specified. Liters and cubic decimeters are the same and milliliters and cubic centimeters are the same. The most important thing is that both volume measurements use the same unit. Pressure can be given in a number of different units. All of these values represent Standard pressure, the atmospheric pressure at sea level. 1atm = 760 torr = 760 mm Hg = kpa = Pa = 14.7 psi Atm is the abbreviation for atmospheres; torr is for Evangelista Torrecelli ( ). Torrecelli s work with Galileo led him to create the first mercury barometer. When Torrecelli upended a glass tube full of mercury into a dish of mercury, the liquid level fell to about 760 mm. Torrecelli s observations of the daily changes in the level of mercury in the tube led to the concept of changing atmospheric pressure. Notice that both torr and mm Hg are equal, 760 torr = 760 mm Hg (the Hg is mercury). These values are always equal. The next unit is the SI (System International) for pressure. It is the kilopascal, kpa. The last is the unit with which you may be most familiar. It is pounds per square inch, or psi. Dalton s Law of Partial Pressure Dalton s Law states that the total pressure of a gas is equal to the sum of its partial pressures. Dry air at sea level is composed mostly of Nitrogen (78.1%), Oxygen (20.9%) and Argon (0.9%). Dalton s Law of partial pressure uses the following formula: P total = P 1 + P 2 + P 3 In this equation, P total represents the total pressure; P 1, P 2, P 3 and so on (when necessary) represent the partial pressures of each of the different gases. The important thing to remember when solving these problems is that all of your units are the same. Convert when necessary. Example: If I have a balloon with the three gases at the following pressures: N: kpa, O: kpa, and Argon 0.95 kpa, what is the total pressure pushing out on the balloon? P total = P 1 + P 2 + P 3 P total = kpa kpa kpa P total = kpa Dalton s law is also applicable when it comes to gas collection over water. A mixture of gases results whenever a gas is collected by displacement of water. Observe the diagram to the right. Oxygen gas is produced through the decomposition of potassium chlorate. The gas in the bottle is a mixture of oxygen and water vapor. Water vapor is present because water molecules escape from the surface of the liquid and collect in the space above the liquid. When the rate of evaporation equals the rate of condensation, equilibrium is reached. The pressure exerted by the water vapor depends on temperature and is referred to as the vapor pressure of water. Example: A sample of solid potassium chlorate (KClO 3 ) was heated in a test tube and decomposed by the following reaction: 2KClO 3 2KCl + 3O 2 The oxygen produced was collected by displacement method at 22 C at a total pressure of 754 torr. The vapor pressure of water at 22 C is 21 torr. Calculate the partial pressure of O 2 in the gas collected. P total = P O2 + P H2O 754 = X + 21 X = 733 torr

2 Mole fraction: the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. The formula used in determining mole fractions is: X 1 = n 1 /n total = P 1 /P total (use either moles or pressure). Mole fraction has no units. Example: The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O 2 present. X 1 = P 1 /P total X 1 = 156/743 X 1 = Boyle s Law for Pressure Volume Changes Boyle s Law is named for Anglo-Irish chemist Robert Boyle ( ). Boyle s Law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. The formula, ah yes, but before we get to that I want to talk about that I- word from above inversely. The word inversely in this case means as one goes up, the other goes down. As the pressure increases, the volume will decrease and vice-versa. A graph showing an inverse relationship is shown above. OK, now the formula: P 1 V 1 = P 2 V 2 P 1 : 1 st pressure P 2 : 2 nd pressure V 1 : 1 st volume V 2 : 2 nd volume Example: A balloon contains 30.0 L of helium gas at kpa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kpa? P 1 : kpa P 1 V 1 = P 2 V 2 V 1 : 30.0 L (100.0)(30.0) = (25.0)( X ) P 2 : 25.0 kpa = 25.0X V 2 : X 120. L = X Charles Law for Temperature Volume Changes Charles s Law is named for the French physicist and balloonist Jacques Charles ( ). Charles Law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. Note, in Charles Law there is a direct relationship between volume and temperature. The graph of a direct relationship is shown on the right. The formula is: V 1 /T 1 = V 2 /T 2 Note that with Boyle s Law there was an inverse relationship and we multiplied our original values. With Charles Law there is a direct relationship, so we will divide our values. More appropriately, we will cross multiply. V 1 : 1 st volume T 1 : 1 st temperature V 2 : 2 nd volume T 2 : 2 nd temperature Example: A balloon, inflated in an air-conditioned room at 27 ºC, has a volume of 4.0 L. The balloon is then heated to a temperature of 57 ºC. What is the new volume of the balloon if the pressure remains constant? V 1 : 4.0 L V 1 / T 1 = V 2 /T 2 T 1 : 27 ºC = 300 K 4.0 = X. V 2 : X T 2 : 57 ºC = 330 K (4.0)(330) = (300)( X ) 1320 = 300 X 4.4 L = X

3 Gay Lussac s Law (Amontons' Law) for Temperature Pressure Changes Gay-Lussac s Law is named for the French chemist Joseph L. Gay-Lussac ( ). Gay-Lussac s Law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume is kept constant. This law also shows a direct relationship. Thus, as the pressure increases, the temperature will increase and vice versa; and as the pressure decreases, so will the temperature and vice versa. The formula is: P 1 /T 1 = P 2 /T 2 P 1 : 1 st pressure T 1 : 1 st temperature P 2 : 2 nd pressure T 2 : 2 nd temperature Example: The gas left in an aerosol can is at a pressure of 100. kpa at 27 ºC. If the can is thrown onto a fire, what will be the internal pressure of the gas when its temperature reaches 927 ºC? P 1 : 100.kPa P 1 /T 1 = P 2 /T 2 T 1 : 27 ºC = 300. K 100. = X. P 2 : X T 2 : 927 ºC = K (100.)(1200) = (300.)(X) = 300. X 400. kpa = X Avogadro s Law for Mole Volume Changes Avogadro postulated that equal volumes of gases at the same temperature and pressure contain the same number of particles The formula: V 1 /n 1 = V 2 /n 2 For a gas at a constant temperature and pressure, the volume is directly proportional to the number of moles of gas. Example: A 15.5 L sample containing 0.40 moles of oxygen gas (O 2 ) at a pressure of 1 atm and a temperature of 25 C. If all of the O 2 is converted to ozone (O 3 ) at the same pressure and temperature, calculate the volume of ozone (O 3 ). 3O 2 2O moles O 2 x 2 moles of O 3 = 0.27 moles O moles of O /0.40 = X/0.27 X = 10. L Homework: General Questions 1. What is standard temperature in Celsius? C In Kelvin? K 2. In all gas law calculations, temperature must be measured in. 3. What is standard pressure in: atm torr psi mmhg kpa 4. What does psi stand for? 5. What does atm stand for? 6. What does kpa stand for?

4 Dalton s Law of Partial Pressure: 1. What is Dalton s Law of Partial Pressure? 2. List the three main gases found in the air we breathe and their percentage of the total. 3. What are formulas for Dalton s Law of Partial Pressure? 4. Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen if the total pressure = kpa, the pressure of nitrogen = kpa, the pressure of carbon dioxide = kpa, and the pressure of the trace gases = 0.94 kpa? 5. A gas is collected over water at 25 C. If the vapor pressure of water is 3.2 kpa and the total pressure is kpa, what is the partial pressure of the gas? 6. A balloon contains mostly helium and a little methane. The partial pressure of helium is kpa. If the pressure inside the balloon is kpa, what is the partial pressure of methane? 7. Determine the mole fraction of oxygen if the pressure of oxygen is 430 torr and the total pressure is 760 torr. 8. The total pressure is 1.20 atm. If the mole fraction of nitrogen is 0.856, what is the partial pressure of nitrogen? Boyle s Law 1. What is Boyle s Law? 2. What is meant by vary inversely? 3. Draw a graph showing an inverse relationship. 4. What formula is used for Boyle s Law? 5. A sample of oxygen gas occupies 250. ml at 740. torr pressure. What volume will it occupy at 800 torr pressure? 6. A 2.0 liter container of nitrogen had a pressure of 3.20 atm. What volume would be necessary to decrease the pressure to 1.0 atm? 7. Ammonia gas occupies a volume of 450. ml at a pressure of 720. mm Hg. What volume would it occupy at standard pressure? 8. A 175 ml sample of neon had its pressure changed from 75 kpa to 150. kpa. What is the new volume? 9. A sample of hydrogen at 1.50 atm had its pressure decreased to 0.50 atm producing a new volume of 750. ml. What was its original volume? 10. Chlorine gas occupies a volume of 1.20 liters at 720. torr pressure. What volume will it occupy at 1.00 atm pressure?

5 Charles Law 1. What is Charles Law? 2. What is meant by directly proportional? 3. Draw a graph that shows the direct relationship between volume and temperature. 4. What formula is used for Charles Law? 5. A sample of nitrogen occupies a volume of 250. ml at 25 ºC. What volume will it occupy at 95 ºC? 6. Oxygen gas is at a temperature of 40. ºC when it occupies a volume of 2.30 liters. To what temperature should it be raised to occupy a volume of 6.50 liters? 7. Hydrogen gas was cooled from 150. ºC to 50. ºC. Its new volume is 75.0 ml. What was the original volume? 8. Chlorine gas occupies a volume of 25.0 ml at 300. K. What volume will it occupy at 600. K? 9. A sample of neon gas at 50. ºC and a volume of 2.50 liters is cooled to 25 ºC. What is the new volume? 10. Helium occupies a volume of 3.8 liters at -45 ºC. What volume will it occupy at 45 ºC? Gay-Lussac s Law 1. What is Gay-Lussac s Law? 2. What is the relationship between pressure and temperature? 3. Draw a graph showing the relationship between pressure and temperature. 4. What is the formula for Gay-Lussac s Law? 5. A gas has a pressure of 6.58 kpa at 540. K. What will the pressure be at 210. K if the volume does not change? 6. The gas in a container has a pressure of 300. kpa at 27 ºC. What is the pressure if the temperature is lowered to 173 ºC? 7. The pressure in an automobile tire is 200. kpa at a temperature of 25 ºC. At the end of a journey on a hot sunny day the pressure has risen to 223 kpa. What is the temperature of the air in the tire? 8. The gas in a balloon has a pressure of 250. kpa at 18 ºC. What will the temperature be if the pressure rises to 294 kpa? 9. A gas confined in a rigid container exerts a pressure of 35.5 kpa at a temperature of 19 ºC. What will the pressure of the gas be if it is cooled to a temperature of -28 ºC?

6 Avogadro s Law 1. What is Avogadro s Law? 2. What is the relationship between moles and volume? 3. Draw a graph showing the relationship between moles and volume. 4. What is the formula for Avogadro s Law? 5. If 2.5 moles of a gas have a volume of 6.0 L, what volume would 3.5 moles have at the same temperature and pressure? L of a gas is known to contain mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)? 7. A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.) grams of oxygen has a volume of 24.8 liters. What is the new volume if 36.0 grams of helium is added and the temperature and pressure remain constant?